Search: id:A119712
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%I A119712
%S A119712 0,1,6,23,64,129,222,345,502,695,924,1193,1502,1853,2246,2687,3172,3705,
%T A119712 4286,4917,5600,6333,7118,7957,8848,9797,10800,11861,12978,14153,15386,
%U A119712 16681,18034,19447,20922,22459,24060,25723,27448,29239,31094,33015
%N A119712 a(k) is the smallest integer n such that the k-th difference of the partition 
               sequence A000041 is positive from n onwards.
%C A119712 The first entry in considered to be indexed by zero. For example, the 
               third difference A072380 starts with -1,1 and continues alternating 
               in sign till the 24th entry, from which point it is positive.
%C A119712 Using a different definition of the difference operator, this sequence 
               has also been given as 1,8,26,68,134,228,352, etc
%D A119712 I. J. Good, Problem 6137, American Mathematical Monthly 1978 pages 830-831
%D A119712 Hansraj Gupta, Finite Differences of the Partition Function, pp. 1241-1243.
%D A119712 A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 
               (1988), pp. 237-254
%F A119712 Odlyzko gives an asymptotic formula a(k)~(6/(Pi)^2) * (klogk)^2
%p A119712 with (combinat): DD:= proc(p) proc(n) option remember; p(n+1) -p(n) end 
               end: a:= proc(n) option remember; local f, k; if n=0 then 0 else 
               f:= (DD@@n)(numbpart); for k from a(n-1) while not (f(k)>0 and f(k+1)>
               0) do od; k fi end: seq (a(n), n=0..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Jul 20 2009]
%Y A119712 Sequence in context: A026817 A162267 A009017 this_sequence A005745 A045618 
               A038737
%Y A119712 Adjacent sequences: A119709 A119710 A119711 this_sequence A119713 A119714 
               A119715
%K A119712 nonn
%O A119712 0,3
%A A119712 Moshe Newman (moshnoiman(AT)gmail.com), Jun 11 2006
%E A119712 a(11) - a(41) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 20 
               2009

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